A floor has two square-shaped designs. The area of the second square-shaped design is nine times greater than the area of the first square-shaped design. Which statement gives the correct relationship between the lengths of the sides of the two squares?

- anonymous

- schrodinger

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- anonymous

these are the options...
The length of the side of the second square is 3 times greater than the length of the side of the first square.
The length of the side of the second square is 12 times greater than the length of the side of the first square.
The length of the side of the second square is 9 times greater than the length of the side of the first square.
The length of the side of the second square is 6 times greater than the length of the side of the first square.

- anonymous

since \(A=l^2\) and \(A'=l'^2\)
when \(A=9A'\)
sub them in to get the relationship between l and l'

- anonymous

what am i supposed to sub in?

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## More answers

- anonymous

the l and l '
like this:
\(A=9A'\)
\(l^2 = 9 l'^2\)

- anonymous

im like really slow and have no idea wut im doing.-_-

- anonymous

lol. i guess i'll try to do it step by step.
since \(A=l^2\),
\(A_1=l_1^2\) (this is the first square)............(1)
\(A_2=l_2^2\) (this is the second square)........(2)
since the area of the second square is nine times the first, (it's the only given condition, so we start from that.)
\(A_2=9A_1\)
subbing (1) and (2) into it, we get,
\(l_2^2=9l_1^2\)|
what did you get after taking thesquare roots of both sides?

- anonymous

sorry im back and thank you.

- anonymous

Just take the square root both the sides and tell us what you got as @Shadowys said above..

- anonymous

Getting ?? @Brianna9898

- anonymous

I have no idea!

- anonymous

Are you getting till here"
\[l_2^2=9 l_1^2\]

- anonymous

why is there a 1 & 2 at the bottom

- anonymous

See when you will take square root you will get like:
\[\large \sqrt{l_2^2} = \sqrt{9 l_1^2}\]
Can you tell what is this:
\[\large \sqrt{l_2^2} = ??\]

- anonymous

... and how am I supposed to square root an l ??

- anonymous

Oh that..
\(l_1\) is showing length of first square.
\(l_2\) is for length of second square.

- anonymous

you can actually..
See,
What is square root of this:
\[\large \sqrt{2^2} = ??\]

- anonymous

2

- anonymous

Similar way what will be square root of this:
\[\large \sqrt{l_2^2} = ??\]

- anonymous

\[l\]

- anonymous

??

- anonymous

Or you can say \(l_2\)..
Good..

- anonymous

Similarly can you tell for:
\[\large \sqrt{9l_1^2} = ??\]

- anonymous

so you have to keep the 2 at the bottom

- anonymous

the one and two are sub scripts to differentiate between the first length and the second, thus, 1 and 2 respectively.

- anonymous

see, 1 and 2 is differentiating lengths of the two square you are given with, so don't think here of just l think here of \(l_1\) and \(l_2\)..

- anonymous

so it would be \[9l _{1} ??\]

- anonymous

You forgot to take square root of 9.
\(l_1\0 is good though..

- anonymous

What is square root of 9?

- anonymous

3

- anonymous

Yep after square root you will get like:
\[\large l_2 = 3 \times l_1\]

- anonymous

So, which answer choice is this?

- anonymous

the first one?

- anonymous

Well Done...

- anonymous

And give all the thanks to @Shadowys

- anonymous

yayyy! thank you guys for helping me!

- anonymous

I don't even know how to give a medal on this thing

- anonymous

Are you seeing best response after shadows post ?/
Just click that..

- anonymous

oh okay, can I give a medal to two ppl?

- anonymous

No, just only one..

- anonymous

On one post you can give medal to one only..

- anonymous

thanx for the medal @Shadowys !

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